YES O(n^2) TRS: {f(c(s(x), y)) -> f(c(x, s(y))), g(c(x, s(y))) -> g(c(s(x), y))} Natural interpretation: Strict: {f(c(s(x), y)) -> f(c(x, s(y))), g(c(x, s(y))) -> g(c(s(x), y))} Weak: {} Interpretation class: deltarestricted [g](delta, X0) = + 0*X0 + 0 + 1*X0*delta + 0*delta [s](delta, X0) = + 1*X0 + 2 + 0*X0*delta + 0*delta [c](delta, X1, X0) = + 0*X0 + 1*X1 + 0 + 2*X0*delta + 0*X1*delta + 0*delta [f](delta, X0) = + 1*X0 + 0 + 3*X0*delta + 0*delta g_tau_1(delta) = delta/(0 + 1 * delta) s_tau_1(delta) = delta/(1 + 0 * delta) c_tau_1(delta) = delta/(1 + 0 * delta)c_tau_2(delta) = delta/(0 + 2 * delta) f_tau_1(delta) = delta/(1 + 3 * delta) Qed